Longitudinally polarized Z Z scattering at a muon collider

Measuring longitudinally polarized vector boson scattering in, e.g., the $ZZ$ channel is a promising way to investigate the unitarization scheme from the Higgs and possible new physics beyond the Standard Model. However, at the LHC, it demands the end of the high-luminosity-LHC lifetime luminosity, $3000\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$, and advanced data analysis technique to reach the discovery threshold due to its small production rates. Instead, there could be great potential at future colliders. In this paper, we perform a Monte Carlo study and examine the projected sensitivity of longitudinally polarized $ZZ$ scattering at a TeV scale muon collider. We conduct studies at 14 and 6 TeV muon colliders respectively and find that a 5 standard deviation discovery can be achieved at a 14 TeV muon collider, with $3000\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of data collected. While a 6 TeV muon collider can already surpass high-luminosity LHC, reaching 2 standard deviations with around $4\text{ }\text{ }{\mathrm{ab}}^{\ensuremath{-}1}$ of data. The effect from lepton isolation and detector granularity is also discussed, which may be more obvious at higher energy muon colliders, as the leptons from longitudinally polarized $Z$ decays tend to be closer.